
§
17.2
Identities
µ
,
0×601=8
curl
grad
=3
If
É
is
conservativ e
,
i.e
-5=001
for
some
¢
Let
¢
,
4
be
smooth
scalar
fields
then
☐
✗
=
☐
xioos-o.ie#isirrotational
.
and
¥
,
I
be
smooth
vector
fields
lil
Px
*
E)
=
ply
.
E)
-
p2É
(
curl
curl
=
grad
div
-
Laplacian
)
(a)
71441 =474+4701
grad
4--84=1,1×4
,
4%-41
(b)
7.
*
E)
=
4)
•
Éto
•
E)
dive
=
☐
•
É=
+
+5¥
a
8×11051--1741*1=>+417×1 -7
(d)
V.
(-7×8)=6×1--7
.ci
-
E.
COXE
,
cure
É
=
☐
×
=
2
,
I
,
Iz
I.
÷
:L
(e)
8×1
✗
E)
=
6
.ci/E-ci.p--T
-
G.
E)
E-
(
F-
•
7)
É
Laplacian
operator
0--02=8.0
8201
=
p.hu/)--divgrad0
f-
I
☐
(
É
.ci/----xlPxaJ-cixl0xEi
+
(
E.
a)
Etta
.ME
=
lot
¢
+
¥ 01
(g)
p
.
(8×-7)=0
div
curl
=o
ÑÉ
=
(04-1,045,51--3)
.
CfÉ=TxÉ
.ie
.
E-
cure
E.
then
diva
:o)
(
G-
•
0
)É=G
,
+
GREY
-16,3¥